Contribution à l'analyse statistique des mesures en chambres réverbérantes

8/15/2019 Contribution à l'analyse statistique des mesures en chambres réverbérantes

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χ2


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θ̂

θ̂

X 2

√ X

X X


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N

S


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N

N

σdB

σdB

σdB

σdB


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N

N

[690

; 710

]

N


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a

b

d

E x

E y

E z

k2 k = 2πf/c

m

n

p

f

ω = 2πf

ω

mnp

E x =

jωµ

k2mn

nπ

b H 0 cos(

mπ

a x) sin(

nπ

b y)sin(

pπ

d z )E y = − jωµk2mn

mπa

H 0 sin(mπa

x)cos(nπb y)sin( pπ

d z )

E z = 0

,


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= 0 = 8.85

µ

= µ0 = 4π10

−7

kmn

kmn =

mπa2

+

nπb2

.

mnp

E x = − 1k2mnmπa

pπd

E 0 cos(mπa

x) sin(nπb y)sin( pπ

d z )

E y = − 1k2mnnπb pπd

E 0 sin(mπa

x)cos(nπb y)sin( pπ

d z )

E z = E 0 sin(mπa

x) sin(nπb y)cos( pπ

d z )

.

f mnp = c

2

m

a

2+

n

b

2+

p

d

2,

c

f 0i

mnp mnp m.n.p

0np m0 p m.n p = 0 mn0 m.n p = 0

110 011 101

f mnp (m,n,p)

f = f mnp

mnp mnp m ≥ 1 n ≥ 1

p ≥ 1

f

f

N (f ) = 8πV

3λ3 ,

V

λ

λ = c/f

f 3


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n(f )

n(f ) = dN

df =

8πV f 2

c3 ,

nMHz(f )

N (∆f )

∆f

nMHz(f ) = 9.3 × 10−7V f 2MHz ,

N (∆f ) = 9.3 × 10−7V f 2MHz × ∆f MHz .

f mnp

σ

µ

Rs

δ s

Rs = 1

σδ s=

πµf

σ ,

δ s = 1√

πµσf .

P

Rs H

P = Rs

2

S

| H |2dS,

S

σ < ∞

∆f Qi

f 0i

f 0i±∆f Qi/2

f 0 ± ∆f Qi/2

f


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∆f Qi

Qi i

∆f Qi = f 0iQi

.

Qi = 2πf 0iW iP i

W i P i i

P i

Qi

Qi

Qi

λ/2

Q

i

Qi

∆f Q

f

N (∆f Q) = 8πV f 3

c3Q .

Q


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E (r) =

4π

F (Ω)e j k(Ω).rdΩ,

j

j2 = −1

r

F

Ω

k

ur Ω

F

Ω

F (Ω) = F θ(Ω)uθ + F φ(Ω)uφ,

uθ uφ

k

( )k Ω1

dΩ

F

1

F uθ θ 1

F uφ φ 1

θ

φ


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Ω

F (Ω)

F θ(Ω) F φ(Ω)

F θ(Ω) = f θR(Ω) + jf θI (Ω)

F φ(Ω) = f φR(Ω) + jf φI (Ω).

F θ F φ

f θR f θI f φR f φI

N (µ, σ2

)

µ = 0

σ

pΩ pΩ(Ω) = 1/4π

< E (r) >

F (Ω)

E (r) = 0.


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r

| E (r)|2 = 16πσ2

| H (r)|2

= 16πσ2

η2

,

η =

µ/

η = 120π


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N


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N

N


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Q


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λ/2


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N

N

N

N

N

N

N


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E x E y E z

E x = E xr + jE xi

E y = E yr + jE yi

E z = E zr + jE zi

.

µ = E xr = E yr = E zr = E xi = E yi = E zi = 0,

σ

σ2 = E 2xr = E 2yr = E 2zr = E 2xi = E 2yi = E 2zi = E 20

6 ,

E 20 ≡ | E (r)|2

E x

f (E xr) =

1σ√ 2π

e−E2xr2σ2

f (E xi) = 1σ√ 2π

e−E2xi2σ2 .

E R

E T P


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Contribution à l'analyse statistique des mesures en chambres réverbérantes